Question

The air inside a balloon can be modeled by the equation P = P atm + kV where V is the volume of the balloon, and k is a value that depends on the material of the balloon. If a balloon with a k value of 10,000Pa/m3 is inflated to a volume of 15m3 with air at 300K, what is the pressure inside the balloon, how many moles of air are inside the balloon, and how much work did that inflation take? (hint: draw the PV diagram of this process)

Answer 1

The pressure inside the balloon is given as

V_initial = 0, V_final = 15 m³

Pressure inside the balloon when its volume is 15m³ = P = P_atm + 10000x15 = 101325 + 150000 = 251325 Pa

To find out the moles of air inside the balloon

PV= nRT

n= PV/RT =

To find out the work done, we need to find out area under the curve of figure shown above.

Area I: (1/2)x (P_f-P_i)x dV =

Area II : P_i x dV =

Total Area = Area I + Area II = 2644875 J

Net work done = 2644.87 kJ